If you need it to be filtered by user, then I would suggest going for the contacts icon in intercom, search for the specific user, and view all their conversations manually.

Not aware of any filter parameter for the user in other reports.

Thank you for the response! For what it's worth, I was able to find a workaround for this. Sharing in case anyone is interested:

• Create a custom report
  • Filter to "Conversation started" and add your date range
  • Select Metric = Conversation Volume
  • Select your preferred chart type
  • Select "View by" = Time (you determine monthly, weekly, etc.)
  • In the top right corner of the chart (before saving) click on the drop-down menu and select "Export Chart Data"
  • The exported spreadsheet shows you every unique conversation started during your date range along with other data like the user name, email address, and when the conversation was closed.

This report gave me way more information than I needed, but I was able to delete, sort, and split some columns to get the report I needed!